Suppose Samantha is walking at a constant speed of 0.5 miles every 6 minutes from her house to a coffee shop located 1.3 miles away. Tina is biking at a constant speed of 0.25 miles every 1.5 minutes to the same coffee shop from her office 2.5 miles away from the coffee shop. Both girls left for the coffee shop at the same time. How many minutes does it take Samantha to walk 1 mile? 12 Preview How many minutes does it take Tina to bike 1 mile? 4.5 Preview Write a function k k that determines the number of miles Samantha has walked in terms of the number of minutes since she started walking, t t. Preview Write a function m m that determines the number of miles Tina has biked in terms of the number of minutes since she started biking, b b. Preview Who reaches the coffee shop first?

a) It takes Samantha 12 minutes to walk 1 mile

b) It takes Tina 6 minutes to bike 1 mile

c) k (t) = 0.083t

d) m (t) = 0.167t

e) Tina arrives befora Samantha

Step-by-step explanation:

a) How many minutes does it take Samantha to walk 1 mile?

This is a direct rule of three problem. So:

6 minutes - 0.5 miles

x minutes - 1 mile

x = 6/0.5 = 12 minutes

It takes Samantha 12 minutes to walk 1 mile

b) How many minutes does it take Tina to bike 1 mile?

Quite similar to a)

1.5 minutes - 0.25 miles

x minutes - 1 mile

x = 1.5/0.25 = 6 minutes

It takes Tina 6 minutes to bike 1 mile

c) Write a function k that determines the number of miles Samantha has walked in terms of the number of minutes.

We know that it takes 6 minutes for Samantha to walk 0.5miles. To build our function k, we need to know how many miles Samantha walks a minute.

So

6 minutes - 0.5 miles

1 - minutes - x miles

x = 0.5/6 = 0.083 miles

So the number of miles in function of t is

k (t) = 0.083t

d) Write a function m that determines the number of miles Tina has biked in terms of the number of minutes since she started biking

Same logic as c). So:

1.5 minutes - 0.25 miles

1 minute - x miles

x = 0.25/1.5

x = 0.167

So the number of miles in function of t is:

m (t) = 0.167t

e)

Samantha will arrive when k = 1.3, so:

0.083t = 1.3

t = 15.66 minutes

Tina will aririve when m = 2.5, so:

0.167t = 2.5

t = 14.9 minutes

Tina arrives befora Samantha